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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Quantum Mechanics

MP 1.1: Vortrag

Dienstag, 16. März 2010, 08:30–08:55, JUR H

Linear phase-space representations of quantum mechanics with minimal uncertainty in position — •Edmund Menge¹ and Hajo Leschke² — ¹Uni Mainz — ²Uni Erlangen

Quantum mechanics with a non-zero uncertainty in position can be generated by a one-parameter generalisation of the canonical commutation relation of ordinary quantum mechanics. This generalisation may be, for example, used in "Quantum Loop Gravity". For such a quantum mechanics with non-zero uncertainty in position a class of linear phase-space representations is defined, covering the well known phase space representation of Weyl, Wigner and Moyal as a limiting case. Applying the Lie-Trotter formula, these representations lead to a transcription of the new Schrödinger-Semigroup as a sequence of finite-dimensional integrals. These integrals can be informally be interpreted as a phase-space path integral.